Affine transformation crossed product like algebras and noncommutative surfaces
Mathematical Physics
2009-03-16 v1 High Energy Physics - Theory
math.MP
Quantum Algebra
Representation Theory
Abstract
Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate representations of *-algebras, geometry of algebraic surfaces, dynamics of affine transformations, graphs and algebras coming from a quantization procedure of Poisson structures. In particular, algebras related to surfaces being inverse images of fourth order polynomials (in R^3) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.
Keywords
Cite
@article{arxiv.0903.1925,
title = {Affine transformation crossed product like algebras and noncommutative surfaces},
author = {Joakim Arnlind and Sergei Silvestrov},
journal= {arXiv preprint arXiv:0903.1925},
year = {2009}
}